OpenVOGEL/Validation

=Validation cases= Validating software is an essential part of the development process. Software should not be use in practical applications without being confident that the results will not be far from reality. This chapter comprises the formal validation of OpenVOGEL's calculation core and is meant to provide sufficient evidence of the program's capability to predict aerodynamic loads, so as to support its application in real cases.

It is a fact that no software will ever provide an exact solution to a particular problem, and how intricate and complete our calculation model could be, there will always be some disagreement with reality. To mitigate this, the validation process will provide us an indication on the level of accuracy for different cases. For some models the accuracy might be very good, and for others it might be unacceptable. It could also be that the accuracy will be acceptable only under a certain subset of the problem's independent variables. Therefore it is important to study as many different configurations as possible so as to identify the situations that lay outside or at the boundary of the theoretical and numerical models.

The validation process can be split in two parts:
 * Validation of the theoretical method: are we using the right assumptions?
 * Validation of the numeric algorithms: is the code well written?

To answer these question, several test cases are going to be presented and analyzed in this section. We will start the validation with a wind tunnel test done in the year 1951 by NACA (currently NASA) at the Ames Aeronautical Laboratory. The model in this experiment is expected to be at the boundary of the our calculation capability since it treats a very low aspect ratio and high sweepback wing. For this case, the low subsonic speed might also give us an indication of how good a simple compressibility correction can be.

After having gained some confidence in the calculation core with the NACA model, we will go to the more conventional case of a low aspect ratio rectangular wing using data from the RAE-916 report (back to the year 1967).

As conclusion of both cases we will see how Tucan in combination with XFoil is very good at predicting the main aerodynamic forces on lifting surfaces up to moderate incidence angle.

The validation will then be focused on closed bodies. The first model will be a simple sphere, which will only be compared against theoretical results as Tucan does not handle flow separation. Finally, it is the idea to compare the static pressure prediction along a conventional fuselage using data from a more complex CFD model.

All validation cases are conform to calculation core version 2.1-2020.05 (this corresponds to the serial number prompted at the beginning of each calculation).

NACA RM-A51G31 technical report
Comparing results against the measurements in a wind tunnel is one of the best alternatives we have, because they were obtained using real air.NACA RM-A51G31 documents a very interesting wind tunnel test of a low aspect ratio wing at increasing Mach numbers. Since Tucan is intended for low speed aerodynamics, the lowest Mach of 0.25 has been selected for this test.

The model in Tucan consist of a flat lifting surface of the same overal dimensions as in the real model:

Remarks

 * In order to correct the compressibility effects, the Prandtl–Glauert transformation formula for 2D cases is used.


 * The panels are uniformly spaced in span-wise direction and the number of panels is as follows:


 * The simulation in Tucan was set up using the next parameters:

Lift coefficient $$C_L$$
In the next table the lift coefficient prediction from Tucan for the wake being shed from the trailing edge only (no wing tips) are compared against the NACA experiment. The values from the experiment have been extracted using pixels from the graph with the given accuracy.

What we obtain as result is what we were expecting. The lift is predicted as a linear function of the incidence angle, but it does not drop after flow separation because the method we are using is unable to do this. The lift slope is accurately predicted and this gives the first indication that the algorithms are correct.

Drag coefficient $$C_D$$
For the drag coefficient XFoil has been used to obtain the airfoil skin friction component at a Reynolds number of 4.000.000 to match the wind tunnel test conditions. The XFoil prediction at zero lift accounts for the total drag at zero incidence angle, and it is impressively accurate. As the incidence increases, the induced drag component predicted by Tucan takes over. The correlation is very good at low incidence, and fairly good at moderate incidence. At high incidence below the separation zone, the induced drag predicted by Tucan is considerably below the wind tunnel measurements and cannot be used.

It is interesting to note that for this model the drag prediction is much more consistent with reality when the wake shedding is done from the trailing edge and the wing tips (and not only from the trailing edge). This might have to do with the sharp sweep-back of the model (it is known that high sweep in delta wings causes leading edge flow separation), although it could also be that we are masking a different mechanisms by just adding more vorticity to the flow. This was briefly discussed in the tutorial about lifting surfaces: the extension of the wake shedding edge is an extra independent variable in the problem that we have to control manually (the so named "Kutta condition").

For the sake of practicty it does make sence to add more shedding if this seems to correlate better with results. In fact, scientists do this kind of things all the time when they don't have a solid evidence about something. Unfortunately, there is not enough data to know how the error is attributed to each of the two information sources (XFoil and Tucan's induced drag prediction algorithm). This could be done in the future with a CFD model. If the data extracted from the plot is correct, the laminar bubble predicted by XFoil seems to last too long, and maybe XFoil is thus also underpredicting the skin drag.

RAE-916 technical report
Technical report RAE-916 describes a series of wind tunnel experiments on very low aspect ratio wings. For this validation case the AF/1 wing case has been selected, which corresponds to a rectangular wing of aspect ratio 4 and symmetrical RAE-101 airfoil. The reported Reynolds number is 1.600.000, and for the Tucan model an XFoil polar at Reynolds 1.000.000 was used (expecting a slight disagreement there).

Remarks

 * For this model, no compressibility corrections were done (due to the low speed of 125ft/s).


 * The panels are uniformly spaced in span-wise direction and the number of panels is as follows:


 * The simulation in Tucan was set up using the next parameters:


 * The wing tips of the RAE model were a bit rounded, something that has not been modeled in Tucan (due to the meshing limitations).

Lift coefficient $$C_L$$
The predicted lift coefficient shows an excellent agreement with the experimental data. For this rectangular model the TE model also provides a more accurate description of the lift.

Drag coefficient $$C_D$$
For this rectangular wing the Tucan TE model provides a more accurate description of the drag than the TE+WT model (in contrast to the NACA model, where the wing tip wake shedding positively contributed to higher accuracy). This evidences that a full wake sheding is not always more realistic.

The two cases presented here suggest that the more the sweep-back the more wing tip shedding we need to improve the accuracy. However this cannot be taken as conclusion without analyzing more cases in between and higher aspect ratios.

Thick bodies: potential flow around a sphere
The potential flow around a sphere can be solved analytically, and it is therefore a good reference for testing thick bodies. The analytical solution is

$$C_p=1-9/4 cos(\theta)$$.

Therefore, we should expect 1 at the stagnation point, and -1.25 at the top. The current algorithm used to find the local surface velocity is based in a estimation of the circulation gradient using least squares. Based on that velocity, the pressure is computed using Bernoulli's equation. The next graph shows how Tucan is currently able of approaching the Cp over the surface. The model consisted of 2400 quadrilateral panels. These results correspond to kernel versions 2.0 and higher (before that, the algorithm was not suitable).